# Math Help - parametrization and stokes's theorem

1. ## parametrization and stokes's theorem

Let $F (x, y, z) = 6yx^2$i + $2x^3$j + $6xy$k, and $C$ be the curve of intersection of the hyperbolic paraboloid $z = y^2 - x^2$ and the cylinder $x^2 + y^2 = 25$ oriented counterclockwise as viewed from above.
(i) Obtain a parametrization of the curve $C$ and use the result to evaluate $\int_{C} F \cdot d$r.
(ii) use Stokes's Theorem to evaluate $\int_{C} F \cdot d$r.

2. See the attachment.

If you have trouble visualising the curve you can see the animation

motion on a saddle on my web site Calculus 3